As an associate economist working for a consulting firm, you have been assigned to analyze some information regarding a proposal to build a dam. Your supervisor has provided the following information to get you started:

• Net benefits from the dam are valued at $4.0 million during the first year of operation.

• The dam will last for 20 years.

• Net benefits will fall at an annual rate of 1 percent.

• The appropriate discount rate is 5 percent.

• If the dam is built, it will destroy a wilderness area, which has been determined to have an annual net value of $2.0 million at the time the dam begins operations.

• If the dam is not built, the wilderness area will increase in value at a rate of 2 percent per year over the next 40 years.

a. How can one account for changes in annual benefits or costs over time in a discounting framework? What shortcut formula can we use and how does one adjust the formula to account for growth or decay in benefits or costs over time?

b. Compute the net present value of the dam including the environmental damage that would be caused. In doing so, assume that the dam will last 20 years, but that the environmental damages will be estimated over a 40 year time horizon. Show your work. 

c. Is it economically justifiable to build the dam? Why or why not?

d. In computing the $4 million in first year net benefits from the dam mentioned above, the evaluators included a secondary market benefit – increases in the output and revenues of agricultural suppliers resulting from increases in expenditures by farmers on supplies (e.g., seed and machinery). Should these secondary benefits have been included? Why or why not?